[BUG] /resume picker shows summarization prompt text instead of actual summaries for agent sessions

Description

The /resume picker displays the literal summarization system prompt text instead of actual conversation summaries for agent/warmup sessions:

Context: This summary will be shown in a list to help users and Claude choose which conversations are relevant. Please write a concise, factual summary of this conversation...

This repeats for many sessions in the list, making it impossible to identify conversations.

Screenshot / Example

❯ claude --resume
  Context: This summary will be shown in a list to help users and Claude choose which conversations are relevant. Please write a concise, factual summary of this conversation. Output ONLY the summary -…
  13 seconds ago · 2 messages · staging

  Context: This summary will be shown in a list to help users and Claude choose which conversations are relevant. Please write a concise, factual summary of this conversation. Output ONLY the summary -…
  17 seconds ago · 2 messages · staging
  
  [repeats for 50+ entries]

Root Cause Analysis

Examining the session JSONL files shows the summarization prompt is embedded in the user message content rather than being a separate system operation:

{
  "type": "user",
  "message": {
    "role": "user",
    "content": [{
      "type": "text",
      "text": "Context: This summary will be shown in a list to help users...\n\nUser: Warmup\n\nAgent: I'm ready to help..."
    }]
  }
}

When /resume extracts the preview text from these sessions, it pulls this prompt text instead of meaningful content.

Steps to Reproduce

1. Use Claude Code with features that spawn agents (Task tool with subagent_type)
2. Generate multiple agent sessions (warmup sessions are created automatically)
3. Run claude --resume or /resume
4. Observe many entries showing the summarization prompt instead of actual summaries

Expected Behavior

• Agent/warmup sessions should either:

1. Not appear in the resume picker (filter by isSidechain: true)
2. Have proper summaries extracted from the actual conversation content (after the warmup exchange)
3. Have the summarization prompt excluded from conversation logging

Environment

• Claude Code version: 2.0.76
• Platform: Linux (Ubuntu)
• Architecture: x86_64

Additional Context

This appears related to but distinct from #10392 (Warmup message injection) which was fixed. The warmup mechanism itself may be working, but the summarization prompt is being logged as conversation content when it should be a system-level operation.

The issue accumulates over time as more agent sessions are created, eventually making the resume picker unusable due to the flood of identical "Context: This summary will be shown..." entries.